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  • $\begingroup$ Wouldn't this be better illustrated by using the simpler set of {1,2,2,2,3,3,3,3}? The expression showing arithmetic mean of that set is identical to the expression showing the expectation value of that variable (if you convert the weighted products into simple sums). $\endgroup$ Commented Jun 13, 2012 at 17:16
  • $\begingroup$ Re: "The expression showing arithmetic mean of that set is identical to the expression showing the expectation value of that variable (if you convert the weighted products into simple sums)" - Yes @Dancrumb, that was the entire point :) $\endgroup$ Commented Jun 13, 2012 at 17:16